Clothing multi-process digital twinning monitoring method

Abstract

The invention relates to the technical field of intelligent manufacturing and production scheduling, in particular to a clothing multi-process digital twinning monitoring method, which comprises the following steps of: establishing process digital twinning by using a colored time delay Petri network and an event dictionary; the processing time distribution and the line changing cost matrix are updated through layered online assimilation; a coupling matrix is obtained through regularization optimal transmission, a dual price vector is calculated, and the upper limit of the capacity of the work-in-process is quantified into the quota of the work-in-process; an anti-fact generator driven by a Koopman operator is called in the rolling prediction window to evaluate increment cost and preferentially sort to generate a release sequence; and locking and issuing the process path according to the quota, implementing reversible fine adjustment based on the deviation, and triggering withdrawal and path change according to the topological structure abstract. The product peak value and the line change loss are reduced, and the stability of capacity utilization and on-time delivery is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing and production scheduling, and in particular to a digital twin monitoring method for multiple processes of clothing. Background Art

[0002] Apparel manufacturing is characterized by small batches, multiple product categories, short lead times, and frequent line changes. Parallel processes, rework and reflow, and equipment collaboration lead to highly unstable WIP distribution and capacity utilization. The significance of multi-process digital twin monitoring lies in connecting monitoring and scheduling with unified process semantics: Accurately representing WIP location, queue evolution, the impact of line changes, and capacity load within the same model, release and rescheduling no longer rely on empirical evidence, but instead operate in a closed-loop manner based on computable, verifiable, and auditable constraints and indicators. This reduces WIP peaks, minimizes the risk of ineffective line changes and delays, and stabilizes the delivery cadence. Summary of the Invention

[0003] In response to the many problems existing in the above-mentioned existing technologies, the present invention provides a method that uses colored time-delay Petri nets to carry process digital twins, drives hierarchical online assimilation driven by event streams, regularizes optimal transmission to align demand and production capacity, and generates dual price vectors and work-in-process quotas; combines Koopman operator counterfactual evaluation and topology structure summary triggering mechanism to complete executable release, reversible fine-tuning and path rerouting, reduces work-in-process and line change losses, and ensures stable delivery.

[0004] A digital twin monitoring method for multiple garment processes includes the following steps: A digital twin of the process, represented by a colored time-delay Petri net, is established. Production signals are mapped into event streams according to a unified event dictionary. The initial state is determined through event playback, and the line change cost matrix is ​​estimated based on this. Hierarchical online assimilation of event streams is performed to update the processing time distribution and line change cost matrix. A topological structure summary is generated based on the work-in-process flow graph. The predicted arrival flow and capacity load distribution are constructed and the coupling matrix is ​​solved through regularized optimal transmission. The Koopman operator is identified to form a counterfactual generator. In the rolling forecast window, the dual price vector is calculated based on the assimilated processing time distribution, line change cost matrix, and coupling matrix. The WIP capacity upper limit is quantified as the WIP quota. The counterfactual generator is called to evaluate the incremental costs of batch release and rescheduling, and the release sequence is generated by optimizing the order. The process path is locked and issued according to the WIP quota, reversible fine-tuning is implemented based on the deviation between the expected state and the execution state, and withdrawal and path rerouting are triggered based on the topology summary.

[0005] Preferably, the initial state is determined by event playback and place invariant consistency check, so that the process digital twin and the event flow maintain conservation consistency in the number of tags and flow direction.

[0006] Preferably, the layered online assimilation updates parameters at the equipment level, workstation level, product level, and batch level, and applies robust weighting to abnormal observations in the event stream to suppress the offset effect on the processing time distribution and the line change cost matrix.

[0007] Preferably, the topology summary is obtained by persistent homology calculation of the work-in-progress flow graph, and the topology change is measured by the bottleneck distance between adjacent time windows to trigger the withdrawal and path rerouting.

[0008] Preferably, the cost matrix of the regularized optimal transmission is composed of a weighted combination of a measure of product attribute differences and a normalized value of a line switching cost matrix, and the coupling matrix is ​​solved by Sinkhorn iteration.

[0009] Preferably, the identification of the Koopman operator is based on an observable function mapping of the state vector, wherein the observable function mapping includes a polynomial expansion of pairs of in-process product position, queue length, device state, and attributes before and after line change, and the stability of the counterfactual generator is ensured by a spectral radius constraint.

[0010] Preferably, the dual price vector is updated using a sub-gradient rule, and spatial smoothing is performed based on the graph Laplace constructed based on the coupling matrix. When the capacity carrying distribution changes slightly, the dual price vectors of adjacent periods are temporally smoothed.

[0011] Preferably, when the WIP capacity upper limit is quantified as WIP quota, the WIP quota is allocated according to bottlenecks and time periods, atomic locking is implemented on process paths across multiple bottlenecks, and the corresponding WIP quota is released according to the path after the job is completed.

[0012] Preferably, the incremental cost is composed of the product of the dual price and the change in work-in-process, the incremental term of the line change cost, the incremental term of the delay cost and the weighted structural penalty term based on the topological structure summary, and adopts a two-level evaluation process, in which the first level is a fast evaluation based on the Koopman operator and the second level is a short-window discrete event simulation refinement evaluation.

[0013] Preferably, reversible fine-tuning includes batch swapping and entry delay operations for batches that have not yet started. The triggering conditions for withdrawal and path rerouting are that the structural index of the topological structure summary exceeds the threshold. Path rerouting selects an alternative path from the set of feasible process paths based on the principle of minimum incremental cost.

[0014] Compared with the prior art, the advantages and beneficial effects of the present invention are: By modeling process semantics using colored time-delay Petri nets and a unified event dictionary, the same-model expression of the impact of work-in-progress, queues, and line changes is achieved.

[0015] By updating the processing time distribution and line change cost matrix through hierarchical online assimilation, the parameters are dynamically converged with the site.

[0016] By constructing a coupling matrix through regularized optimal transmission, the distribution layer alignment of demand distribution and capacity carrying capacity is achieved.

[0017] By calculating the dual price vector, continuous quantification and comparable pricing of congestion intensity are achieved.

[0018] Through work-in-progress quotas and atomic locks, we achieve one-time executable capacity constraints across bottleneck paths.

[0019] Through the Koopman operator and counterfactual generator, fast incremental evaluation of candidate releases and reordering is achieved.

[0020] By triggering withdrawal and path rerouting through topology summary, a structural solution to ring congestion is achieved.

[0021] By preferentially sorting and issuing release sequences in the rolling forecast window, stable release and auditable closed loop are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0023] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present disclosure. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present disclosure.

[0024] like Figure 1 As shown, a digital twin monitoring method for multiple processes of clothing includes the following steps: A digital twin of the process, represented by a colored time-delay Petri net, is established. Production signals are mapped into event streams according to a unified event dictionary. The initial state is determined through event playback, and the line change cost matrix is ​​estimated based on this. The process digital twin uses a colored time-delay Petri net as the semantic carrier for process semantics. Places represent each process step and buffer position, transitions represent events such as arrival, start, completion, and line change, and tags carry color attribute vectors to describe product identification, size, color, fabric, and auxiliary material combinations, as well as process path identifiers. Time delays are used to express processing time and line change duration. This representation allows production status, work-in-progress materials, and equipment occupancy to be uniformly depicted within the same discrete event model, facilitating subsequent assimilation, prediction, and control.

[0025] The event dictionary is used to normalize production signals into event streams. Inbound barcodes and RFID signals are recorded as arrivals, outbound barcodes and RFID signals or manufacturing execution system reports are recorded as completions, the press of a workstation start button or the start of a program is recorded as a start, confirmation of a workstation report or the end of a program is recorded as completion, equipment shutdown and resumption are recorded as shutdown and resumption, respectively, and the start and completion of cutting on the operation panel are recorded as the start and end of a line change, respectively. The event stream includes fields such as timestamp, equipment ID, workstation ID, process number, batch number, product ID, and color attribute vector. To ensure time consistency, a unified timing and lateness window strategy is adopted. Late events are reordered within the window, and events outside the window enter the compensation queue and are corrected in the next cycle without compromising the submitted state.

[0026] The initial state is advanced from the most recent time watermark to the current time through event playback. The core update follows the following expression: , in, Indicates time The tag vector contains the number of work-in-progress in each library; represents the incidence matrix, where rows correspond to places and columns correspond to transitions; Indicates at time The triggered transition vector has elements of 0 or 1. By sequentially triggering events on the timeline and updating the marker vector, the initial state is obtained. This initial state includes work-in-progress distribution, queue length, equipment availability, and attribute pairs before and after the line change. To prevent model drift, structural consistency checking is introduced, using place invariants to verify conservation relationships. When inconsistencies are found, the event segments with the least impact are replayed and repaired.

[0027] The line change cost matrix is ​​used to measure the time and energy consumption of switching from one attribute combination to another. Without changing the process path constraints, the line change cost is modeled as a weighted superposition of attribute differences and allows for attribute interaction terms: , in, and Represent the attribute vectors before and after the line change, and the components correspond to the color, fabric, size and accessories combination, etc. Indicates the An indicator of whether an attribute has changed, which can be 0 or 1; Indicates the and An indicator of whether the two attributes change at the same time, which takes 0 or 1; is the parameter to be identified. Parameter identification uses the least squares method with non-negative constraints and robust weighting of outliers. Training samples are derived from the duration from "line change start" to "line change end" and the corresponding attribute pairs. To improve portability, a shared prior is established for different devices and constraints are applied at the device level, allowing for stable estimation even for workstations with sparse samples. Energy consumption can be modeled in parallel using the same structure for energy efficiency analysis and line change direction penalties.

[0028] The application path of the present invention is as follows: First, the process digital twin carries the mutually exclusive relationship between processes, buffers, and equipment, so that the flow of work-in-process and resource occupancy have computable event semantics; second, the event dictionary normalizes heterogeneous signals into event streams, ensuring that event playback can reproduce the real production trajectory; third, a credible initial state is obtained through event playback, which serves as the starting point for subsequent assimilation and prediction; finally, the line change cost matrix establishes a connection between the product attribute space and the equipment switching cost, providing quantifiable marginal costs for subsequent release sorting, path selection, and line change direction judgment. As a result, the monitoring layer can simultaneously display the work-in-process position, queue changes, and potential line change costs in a single model, and the scheduling layer can quickly evaluate the impact of release and rescheduling based on the initial state as a baseline.

[0029] Compared to solutions that rely solely on empirical rules or a single signal, this step is effective in three ways. First, state consistency: Through event playback and structural consistency verification, the initial state corresponds one-to-one with the actual production record, avoiding misjudgments caused by state drift. Second, cost interpretability: The line change cost matrix uses attribute differences as independent variables, and the coefficients have clear physical meanings, facilitating auditing and maintenance. Third, cross-line migration: Through hierarchical parameter constraints and robust identification, the model can be migrated between different equipment and workstations, reducing the cost of repeated calibration.

[0030] Example: A production line including cutting, sewing, ironing and final inspection is selected as the object. In the process digital twin, the cutting outlet, sewing entrance, sewing buffer, line change resource position, ironing station and final inspection position are all set as warehouses, and arrival, start, completion, line change start and end are set as transitions. The event dictionary defines barcode scanning inbound as arrival, work report and barcode outbound as completion, station start and stop buttons as start and completion, and cutting instructions on the operation panel as line change start and end. The event stream within one shift is collected and time synchronization and lateness correction are performed. Then, event playback is performed, and the initial state is obtained using the above-mentioned update expression. The work-in-progress distribution shows that the work-in-progress in the sewing buffer is higher than that in the ironing entrance. Based on the same data, the attribute pairs of all line change segments are extracted. The attribute dimensions include color, fabric and size. The robust weighted least squares method is used to identify the parameters of the line change cost matrix and non-negative constraints are imposed. The recognition results show that color changes are weighted more heavily than size changes, and the interaction term for simultaneous color and fabric changes is weighted more heavily than the sum of their individual weights. This matrix is ​​applied to the monitoring dashboard to calculate the time costs of candidate releases and potential line change directions in real time, which is used for subsequent priority assessment and path selection. In subsequent rolling cycles, the initial state serves as the starting point for the assimilation and prediction process. The line change cost matrix is ​​updated incrementally with each new sample to ensure cost assessments are consistent with those in the field.

[0031] Preferably, the initial state is determined by event playback and place invariant consistency check, so that the process digital twin and the event flow maintain conservation consistency in the number of tags and flow direction.

[0032] The process digital twin uses a colored time-delay Petri net to represent the relationships between processes, buffers, and equipment occupancy. Event replay uses event time as the trigger, triggering corresponding transitions for arrival, start, completion, and line changeover start and end. This drives the migration of tags between locations and reconstructs the current distribution of work-in-progress and queues. Core updates follow the tag update formula: , in, For the moment The tag vector of (the number of work-in-progress in each library), is the incidence matrix (rows correspond to places, columns correspond to transitions), For the moment The triggered transition vector (elements are 0 or 1). To avoid repeated rollbacks caused by time disorder, event time watermarks and late windows are used. Late events within the window are placed in the local replay queue, and late events outside the window are placed in the compensation queue and wait for the next cycle to be processed. The consistency check of the place invariant is used to constrain the replay results from the structural level. If there is a vector satisfy: , Then there is a conservation relation for any trigger sequence: , in, is a place invariant vector, whose elements represent weighted aggregation coefficients for each place. In actual implementation, a set of basis invariant vectors is derived offline from the process diagram. The above conservation is verified for each marked vector after each partial replay. If a deviation occurs, the deviation component is recorded and the smallest event segment causing the deviation is located. Prioritize rollback to delete duplicate events, correct cross-device mismatches, or merge broken line change segments, and replay again until the deviation is eliminated. This process ensures the structural correctness of the "count and flow" system and makes the initial state auditable.

[0033] After the initial state calculation is completed, the distribution of work-in-progress, the queues at the entrance of each process, the availability of equipment, and the attribute pairs before and after the line change are obtained. The attribute pairs and duration in the attribute pairs before and after the line change are directly derived from the event segment of "line change start - line change end", which are used for the estimation of the subsequent line change cost matrix. The identification of the line change cost matrix is ​​a mature practice, and it is only necessary to explain in the present invention that: the attribute difference and attribute interaction are used as independent variables, the line change duration is used as the dependent variable, and the least squares method with non-negative constraints and weighted abnormal samples is used for identification, and a shared prior is introduced at the equipment layer to improve the stability of the sample sparse workstation. Since the initial state has been guaranteed by the structural consistency test, the extracted line change samples have high credibility, which avoids the transmission of time deviations caused by missed or duplicate reports.

[0034] The effectiveness of this step is reflected in three aspects. First, state accuracy: The tag update formula and the library invariant formula jointly constrain the values ​​and flow directions of the work-in-progress and the queue to be consistent, eliminating the arbitrariness of "resetting based on experience." Second, data availability: The initial state that has passed the consistency test can be directly used as the starting point for assimilation and prediction, reducing subsequent parameter drift; the filtered line change fragments provide high signal-to-noise ratio samples for cost identification. Third, traceability: Each local replay and repair is bound to a specific event fragment, forming an auditable track, which facilitates quality accountability and process review.

[0035] Example: Select a production line that includes cutting, sewing, pressing, and final inspection. Construct a digital twin of the process, establishing the cutting exit, sewing entry buffer, sewing station resources, pressing entry buffer, and final inspection location as locations. Establish arrival, start, completion, line change start, and line change end as transitions. Collect barcode entry, work report, equipment start / stop, and cutting signals within a shift, and generate an event stream after unified timing. Replay events from the most recent watermark to the current time, triggering each event one by one according to the tag update formula. After the first replay, perform a conservation check on the three sets of invariants, and discover that the weighted sum of one set involving the sewing buffer and pressing entry deviates by 2. Retrieving local events reveals duplicate entries of the same batch at the pressing entry. These are identified as duplicate events, deleted, and replayed, with the deviation reset to zero. This results in the initial state: the sewing entry queue is 8, the pressing entry queue is 4, two sewing stations are idle, and the remaining are occupied or changing lines. Subsequently, 120 corrected "line change start - line change end" segments were extracted and organized into three-dimensional combinations of color, material, and size. A low weight was assigned to abnormal duration samples to complete cost identification. The identification results showed a significant interaction term for simultaneous changes in color and material, indicating that switching this combination on this production line requires more preparation and verification. The initial state and cost results are then passed on to subsequent modules: the assimilation module uses this state as a starting point to update the processing time distribution, and the scheduling module uses the cost matrix to constrain release and line change direction selection.

[0036] Hierarchical online assimilation of event streams is performed to update the processing time distribution and line change cost matrix. A topological structure summary is generated based on the work-in-process flow graph. The predicted arrival flow and capacity load distribution are constructed and the coupling matrix is ​​solved through regularized optimal transmission. The Koopman operator is identified to form a counterfactual generator. This paper considers the event stream as a continuous observation of the process digital twin. Hierarchical online assimilation is used to calibrate the processing time distribution and the line change cost matrix in real time. Observations are from the processing time from "start to finish" and the line change time from "line change start to end". Features include product attributes, equipment and workstation working conditions. A recursive update method is used: , , , in, For the moment The parameter vector contains the estimated coefficients of the processing time distribution and the line change cost matrix; is the actual measured duration; Based on The prediction duration of the feature; is the first-order sensitivity matrix; is the parameter covariance; is the observation noise covariance; is the unit matrix. To suppress the influence of abnormal observations, robust weights are introduced for outlier samples, and a shared prior is set at the device layer to ensure the stability of sample sparse stations.

[0037] The WIP flow graph uses processes as nodes and marked flows as directed edges. The edge weight is the number of passes or the amount of WIP within the window. To characterize structural changes, the topological structure summary is calculated and compared with the previous window to obtain the stability measure of the bottleneck ring and confluence structure. ,in, and is the topological summary of adjacent windows, is the bottleneck distance between the two. This quantity is used to trigger retraction and path rerouting in subsequent control to ensure structural consistency.

[0038] The predicted arrival flow describes the future attributes - the distribution of arrivals on the time grid, and the capacity distribution describes the bottleneck - the processing capacity on the time grid. The two are balanced by regularization to achieve optimal transmission: , in, is the coupling matrix; is the cost matrix, which combines the attribute distance and the normalized line switching cost; is the regularization coefficient; is the entropy term; To predict the arrival flow; For capacity carrying distribution; is a vector of all 1s. This solution ensures that the arrival side and the capacity side are aligned at the distribution level, providing a marginal load baseline for subsequent calculations of work-in-process quotas and dual prices.

[0039] The counterfactual generator uses the Koopman operator for rapid evaluation. First, the state vector is mapped to an observable function to construct features containing pairs of WIP positions, queue lengths, equipment status, and attributes before and after line changes. This is then identified through extended dynamic mode decomposition: , , , in, is an observable function mapping to the state; For the moment Status; and is the empirical moment; is the Koopman operator; is the ridge coefficient; is the number of samples; is the generalized inverse. By conducting short-term advancement, a rapid incremental assessment of throughput, work-in-progress, delays, and line change costs can be given for micro-actions such as “batch release, batch rescheduling, process path switching, and line change direction selection.” Top-ranked candidates then enter short-window discrete event simulation refinement to form highly credible counterfactual results.

[0040] The effects of the above links are reflected in the following aspects: first, the parameters continue to converge with observation, and the processing time distribution and line change cost matrix remain consistent with the on-site situation; second, the topology structure summary provides structural layer monitoring signals to promptly detect the deepening of bottleneck loops and abnormal confluence; third, regularized optimal transmission achieves demand-capacity alignment at the distribution layer, laying the foundation for the allocation of work-in-process quotas and the smooth evolution of dual prices; fourth, the Koopman operator enables micro-action evaluation to have millisecond-level response, providing a computable prior for rolling optimization.

[0041] Example: This step was run on a production line consisting of cutting, sewing, pressing, and final inspection. After collecting an eight-hour continuous event stream, layered online assimilation was initiated. The processing time distribution of the sewing stations converged to the new team level within one hour, and the weight of the interaction term "simultaneous color and fabric change" in the line change cost matrix was increased. A work-in-process (WIP) flow diagram was constructed and a topology summary was generated. Compared to the previous window, the increase in bottleneck distance indicated a deepening of the loop between "sewing buffer and pressing entry." A predicted arrival flow was generated based on sales rhythm and WIP status. The capacity distribution was derived by combining the equipment calendar. A coupling matrix was derived through regularized optimal transmission. The results showed that dark-colored items were concentrated in the second half of the window for pressing capacity. After identifying the Koopman operator, a rapid evaluation of the micro-action of "prematurely releasing dark batches and swapping them with light batches" was performed. The predicted WIP peak decreased and the incremental line change cost was acceptable. The conclusion remained consistent after entering a short-window simulation, serving as the input for release and rescheduling in the next cycle. Through this process, the monitoring interface can simultaneously display parameter updates, structural signals, and distribution alignment results. The dispatching end can use counterfactual evaluation to support release sorting and path selection, forming a closed loop from observation to decision-making.

[0042] Preferably, the layered online assimilation updates parameters at the equipment level, workstation level, product level, and batch level, and applies robust weighting to abnormal observations in the event stream to suppress the offset effect on the processing time distribution and the line change cost matrix.

[0043] The goal of hierarchical online assimilation is to calibrate the processing time distribution and line change cost matrix in real time as the process digital twin continuously receives event streams, so that the parameters simultaneously reflect the capability differences between equipment and workstations, process differences in product attributes, and short-term fluctuations introduced by batches. To this end, each type of duration parameter is represented as the sum of a global baseline and four layers of biases, forming an interpretable and transferable structure. The core decomposition is: , in, Indicates time The parameter vector includes the estimated coefficients of the processing time distribution and the line change cost matrix; is the global baseline; is the device layer bias, index Identification equipment; is the workstation layer offset, index Mark workstations; is the product layer bias, index Identify product attribute combinations; is the batch layer bias, index Identify batches. The four-layer bias is subject to shrinkage constraints and automatically regresses to zero when there is insufficient evidence, ensuring robustness in small sample scenarios. Online assimilation is recursively updated at the granularity of a single observation. For each pair of "start and finish" or "line change start and end" events, a feature pair consisting of the observation duration and the attributes before and after the line change is constructed. The predicted duration and residual are calculated using the current parameters, and then weighted and updated according to the robust weights. The core recursion is: , in, For the measured duration, for the reason The predicted duration of the attribute pair features before and after the line change, Assimilation gain, is a robust weight. Robust weights are used to suppress the influence of abnormal observations and take the form of adaptive thresholds: , in, is the median absolute deviation scale based on the sliding window. Determined by sensitivity and uncertainty, it includes a four-layer bias allocation matrix, distributing residuals to the equipment, workstation, product, and batch layers according to their contribution. Updating the covariance and setting the shrinkage coefficient are common practices in this field and are omitted here. The core purpose is to ensure that high-variance layers receive stronger shrinkage constraints.

[0044] The processing time distribution uses linear links in the logarithmic domain to adapt to positively skewed distributions, and the line change cost matrix is ​​parameterized using attribute differences and attribute interactions as independent variables. The observed attribute pairs before and after the line change are uniformly derived from the state and color attribute vectors of the process digital twin, ensuring consistency between the assimilation caliber and subsequent scheduling. Abnormal observation identification uses two types of signals: one from equipment and workstation self-check flags, such as extreme durations caused by short downtimes; the other from event fragments marked as low confidence after structural consistency verification. These two types of signals act together on robust weights, not discarding data but reducing its impact on the parameters.

[0045] At the implementation level, the equipment and workstation layers share priors to reflect the transferability of the same model of equipment or adjacent workstations. The product layer is characterized by combinations of color, fabric, and size, and the batch layer reflects short-term perturbations in personnel, materials, and the environment. Online assimilation is performed recursively according to the time sequence of events, completing parameter updates approximately every few seconds, forming a lightweight loop that aligns with the rhythm of the event flow. Parameter updates are immediately fed back to the process digital twin for prediction and counterfactual evaluation.

[0046] The above-mentioned layered and robust strategies bring about three types of effects. First, anti-drift: abnormal reporting, temporary shutdowns, and a small amount of missed reports no longer deviate the parameters as a whole, and the residuals are limited to the controllable range of a single update. Second, fast convergence: the batch layer quickly absorbs short-term changes, the product layer and the workstation layer complete the main adjustments within dozens of observations, and the equipment layer maintains a slow and stable drift correction, presenting an overall "fast-medium-slow" time scale decomposition. Third, portability: when a new workstation is online or the first batch of new products enter, the layered structure enables it to inherit the historical knowledge of the equipment and products, and only a small number of batch-level observations are required to achieve usable accuracy, significantly reducing the cold start cost.

[0047] Example: This step is run on a production line that includes cutting, sewing, ironing, and final inspection. After collecting 8 consecutive hours of event streams, layered online assimilation is initiated. In the initial stage, the measured duration of the sewing station increases significantly compared to the historical baseline, and the residual is quickly absorbed into the batch-level bias to avoid misjudging short-term fluctuations as equipment capacity degradation. In the second hour, a certain equipment causes two extremely long observations due to maintenance. The robust weight compresses the weights of the two observations to close to 0.3, and the equipment-level bias is only slightly corrected. The station-level and product-level biases remain basically stable. In the fourth hour, a new color and fabric combination enters production. The product-level bias forms a stable estimate after approximately 20 observations, and together with the line change segments, it supports the incremental update of the line change cost matrix. In the sixth hour, the change of team causes a short-term decrease in sewing duration. The batch-level bias absorbs this change within 30 minutes and then gradually regresses. By the end of the full cycle, the logarithmic domain variance of the processing time distribution for the two key processes, sewing and ironing, decreased by approximately 20% and 15%, respectively. The confidence intervals for the color-fabric interaction term in the line change cost matrix converged significantly. Instant parameter writeback enabled the prediction module to evaluate releases and rescheduling based on the latest distribution. This allowed the scheduling side to reduce the number of high-cost line change directions. The monitoring side visualized the evolution of biases at each layer, facilitating dual-line review of processes and equipment.

[0048] Preferably, the topology summary is obtained by persistent homology calculation of the work-in-progress flow graph, and the topology change is measured by the bottleneck distance between adjacent time windows to trigger the withdrawal and path rerouting.

[0049] In digital twin monitoring of multiple apparel processes, the WIP flow graph uses processes as nodes and the directional relationships between WIP passages and waiting times as edges. Edge weights are normalized by the number of passes or average waiting times within a time window. This graph reflects the actual flow and accumulation patterns of materials between processes. To obtain structural quantities that are directly relevant to scheduling and comparable across windows, the present invention uses persistent coherence as a tool to map the WIP flow graph into a topological structure summary, which is used to identify persistent parallel confluences and ring congestion patterns. The topological distance between adjacent time windows is then used to characterize the intensity of structural changes.

[0050] The topology summary is calculated by generating a filter sequence with increasing thresholds based on the WIP flow graph, constructing birth and death trajectories of coherent features, and obtaining a persistence spectrum. To match the scheduling objectives, this paper focuses on the one-dimensional coherent features corresponding to the ring structure. A greater persistence indicates a higher risk of WIP backlog along multiple paths. After matching the topology summaries of adjacent windows, the bottleneck distance is used to measure the intensity of structural changes, which serves as a criterion for triggering withdrawal and path rerouting.

[0051] The core volume is defined as follows: , , in, Homology Durability, and are the birth and death levels, respectively; and is a summary of the topology of adjacent time windows (persistence graph); is the bottleneck distance; is the optimal match between the two graphs. The trigger logic is written as: , in, is the structural change threshold, is the persistence threshold, and both are calibrated by the quantiles of the historical distribution. The above expression is only used to define the trigger quantity. The specific threshold calibration and numerical solution adopt the common methods in this field.

[0052] In actual implementation, the time window length and step interval are consistent with the monitoring refresh cycle. To minimize the impact of directionality on coherence calculations, the WIP flow graph is undirected or bidirectionally weighted and symmetric when calculating the loop structure, maintaining sensitivity to large-scale cycles. The topology summary contains three types of information: feature count, total persistence, and the contributing edge set of high-persistence paths. The contributing edge set is extracted from the edge weight-feature relationship using a back-substitution algorithm to locate the process connections that contribute most to the loop structure, providing actionable objects for subsequent withdrawal and path rerouting.

[0053] The mapping of topological quantities to control follows the principle of "isolation first, then rerouting." When the trigger signal is true, the unstarted batches located on the high-durability loop are first filtered out according to the contribution edge set to form a withdrawal list. The withdrawal operation does not change the continuity of the already started operations. Subsequently, in the set of feasible process paths, the topological impact of each candidate path is quantified using counterfactual evaluation, and alternative paths that reduce the bottleneck distance without increasing the cost of line change and the risk of delay are given priority. At the same time, the intensity of topological change is used as a reference for the structural item in the scheduling cost and the adjustment of the work-in-process quota. In the short term, the work-in-process quota on the high-durability loop is tightened to reduce the probability of further aggravation of the loop.

[0054] The effectiveness of this mechanism is reflected in three key aspects. First, the structure is observable: The topological summary quantifies structural phenomena such as "whether ring congestion occurs" and "whether confluence becomes heavier" into comparable scalars and edge sets, facilitating cross-shift and cross-day comparisons. Second, the trigger is explainable: Bottleneck distance and maximum persistence are mapped to specific pathways and batches, and both withdrawals and route reroutes have clear directions and evidence. Third, the coupling is closed-loop: Topological triggering forms a closed loop with work-in-process quotas, dual prices, and counterfactual assessments, avoiding short-sighted adjustments caused by relying solely on local queue length signals.

[0055] Example: Deploy a topology summary module on a production line that includes cutting, sewing, ironing and final inspection. Set the window length to 30 minutes and the step to 5 minutes. In the window from the 3rd hour to the 3rd hour and 30 minutes, the topology summary is calculated, and the loop corresponding to the maximum persistence spans "sewing buffer-ironing entrance-ironing buffer-sewing entrance". The bottleneck distance compared with the previous window is 0.12, which exceeds the threshold of 0.08, and the trigger signal is true. The contribution edge set is located at the two edges of "sewing buffer→ironing entrance" and "ironing buffer→sewing entrance". Based on this, the system generates a withdrawal list, which includes 12 unstarted batches located on the subsequent paths of the above two edges. For each withdrawn batch, the counterfactual evaluation compares two alternatives in the set of feasible process paths: one is to delay entry to the next time grid, and the other is to first execute another sequence with the same fabric as the current one. Evaluation revealed that the second option resulted in a more significant reduction in the expected bottleneck distance without increasing the cost of line changeovers. Based on this, the system generated a rerouting instruction and simultaneously tightened the WIP quota for the paths along the two edges to 0.9 of the original value. In the next window, the bottleneck distance dropped to 0.07, the maximum persistence decreased, and the loop structure began to ease. The withdrawal strategy was subsequently withdrawn, retaining only the rerouting and a slight tightening of the WIP quota. Throughout this process, the topology summary, rerouting list, rerouting, and WIP quota changes were recorded as auditable evidence for process review and equipment collaborative optimization.

[0056] Preferably, the cost matrix of the regularized optimal transmission is composed of a weighted combination of a measure of product attribute differences and a normalized value of a line switching cost matrix, and the coupling matrix is ​​solved by Sinkhorn iteration.

[0057] The present invention uses regularized optimal transmission to align the predicted arrival flow with the capacity load distribution at the distribution layer. The source end is a discrete grid of attributes and time, and the target end is a discrete grid of bottlenecks and time. The coupling matrix describes the distribution intensity of each type of arrival in each bottleneck time period. The key is to construct a cost matrix that fits the process physics so that the distribution follows the constraints of attribute compatibility and line change cost at the same time. Attribute compatibility is measured by attribute embedding vectors, and line change constraints are given by line change cost matrices, and the normalized line change cost is formed by combining the attribute pairs before and after the line change in the digital twin. The attribute embedding vector is consistent with the process genome encoding described above, and is used to characterize the impact of color, fabric, size and auxiliary material combinations on processing and switching.

[0058] The cost matrix is ​​constructed as follows. Let the source unit be , is the arrival of a certain attribute combination at a certain time grid; the target end unit is , is the available capacity of a bottleneck grid at a certain time; the attribute embedding vector is , the bottleneck preference vector is , the bottleneck preference vector is obtained by regressing historical allocation and equipment characteristics. The attribute difference is measured using Euclidean distance: , The normalized line change cost is derived from the line change cost matrix and the attribute pairs before and after the current line change. For the attribute combination planned for processing before the target end unit, the line change cost function is , take the maximum value and normalize: , in, is the upper bound or high percentile normalization constant of the historical line switching cost. The weighted cost is obtained by combining: , in, and is the weight, satisfying Larger Emphasize attribute compatibility, larger Emphasis is placed on suppressing line switching losses. After the construction is completed, the regularized optimal transmission solution is performed: , in, is the coupling matrix, To predict the arrival flow, For capacity distribution, is the regularization coefficient, is the entropy term, is a vector of all 1s. Sinkhorn iteration is used for efficient solution. Let the kernel matrix be: , Then there is a scaling solution . The iterative update is: , , Among them, 0 is element-by-element division, and is the scaling vector. Iterate until the marginal constraints meet the accuracy requirements. To ensure numerical stability, the kernel matrix and scaling vector are conventionally truncated using the logarithmic domain or threshold, which is not detailed here.

[0059] The application significance of this design is reflected in three aspects. First, physical consistency. The attribute difference term prioritizes matching bottleneck periods for homogeneous attributes, and the normalized line switching cost term avoids periods and directions with high line switching costs, reducing unnecessary switching at the distribution level. Second, cross-window comparability. Regularization and normalization stabilize the cost scale, and the coupling matrix can be directly used for expected load and smoothing strategies in different time windows. Third, scheduling availability. The row and column margins of the coupling matrix directly indicate the expected load of each bottleneck in the future time period. They can be used as input for work-in-process quotas and dual prices, and serve as a prior distribution field when evaluating candidate actions.

[0060] Example. On a production line that includes cutting, sewing, ironing and final inspection, the time step is set to 10 minutes, and the arrival flow is predicted to give the arrival volume of color and fabric combinations in the next 6 time grids. The capacity carrying distribution gives the capacity of the two bottlenecks of sewing and ironing in the corresponding time grid. Use historical data to train attribute embedding vectors so that the vector distance between denim fabric and dark color in the sewing bottleneck is smaller, and the vector distance with the ironing bottleneck is larger, reflecting the process sensitivity of the two bottlenecks. Obtain the attribute pairs before and after the line change from the digital twin, obtain the preceding attribute combination of each bottleneck time grid, and calculate the normalized line change cost based on the line change cost matrix. Set weights and satisfy , select a larger one based on the recent line change frequency , in order to reduce the cost of the upcoming large number of cuts. After constructing the cost matrix, the kernel matrix is ​​calculated and Sinkhorn iterations are performed for about 50 times to obtain the coupling matrix. The results show that dark denim is more likely to be assigned to the sewing bottleneck, which is currently in the dark sequence, in the first half of the window, while light-colored woven fabrics are connected to the ironing capacity in the second half of the window, and the row and column margins are consistent with the input distribution. The coupling matrix is ​​aggregated into the bottleneck expected load, which serves as the allocation baseline for the work-in-process quota and as a smoothing reference for the dual price update. Subsequently, in the candidate action evaluation, the system reduces the number of cross-color line change direction selections, and the release sequence is biased towards the same-color first solution. The loop persistence in the topology structure summary decreases, indicating that the loop congestion has been alleviated.

[0061] Preferably, the identification of the Koopman operator is based on an observable function mapping of the state vector, wherein the observable function mapping includes a polynomial expansion of pairs of in-process product position, queue length, device state, and attributes before and after line change, and the stability of the counterfactual generator is ensured by a spectral radius constraint.

[0062] This invention elevates the discrete event evolution of the process digital twin to an observable function space, using linear operators to approximate nonlinear dynamics. This allows for millisecond-level assessment of the incremental impact of micro-actions such as batch release, batch rescheduling, process path switching, and line change direction selection. The state vector consists of the work-in-process position, the queue length at each process entrance, equipment availability and downtime flags, and attribute pairs before and after the line change. These attribute pairs record the previous and next attribute combinations, enabling the linkage of subsequent cost and state responses.

[0063] The observable function mapping consists of a polynomial expansion of the aforementioned state variables, including linear terms, quadratic interaction terms, and interaction terms with pairs of pre- and post-line attributes. Components of different dimensions are normalized to ensure numerical stability. The mapping dimension is set to a sufficient level to express the dominant coupling relationship between the queue and the work-in-process, while not causing excessive dimensionality explosion. Generally, a second- or third-order dimension is sufficient to cover common concurrency and confluence effects.

[0064] The identification of the Koopman operator uses the empirical matrix form of extended dynamic mode decomposition: , , , in, is an observable function mapping, For the moment The state vector of is the number of samples, is the ridge parameter, is the identity matrix, is the generalized inverse. To mitigate the impact of anomalous observations, samples marked as low confidence by equipment self-test or structural verification are weighted less heavily when constructing the experience matrix. This does not alter the framework, but only adjusts the sample contribution. Recognition is performed on a sliding window to accommodate changes in work groups, materials, and the environment.

[0065] In order to ensure the numerical stability of the counterfactual generator in the short term, the spectral radius constraint is introduced. First calculate the spectral radius: , like Exceeding the preset upper limit (According to the prediction step number and refresh cycle settings), perform shrink projection: , in, A small margin is used to ensure that the shrinkage is strictly within the stable region. This process does not change the feature direction, but only scales the amplitude proportionally to avoid divergence during short-term rolling. A linear push is then used to approximate the short-term effect of the micro-motion: , in, The predicted WIP position, queue length, and pre- and post-line change attribute pairs are combined with the assimilated processing time distribution and line change cost matrix to calculate throughput, WIP peak, delay, and line change cost increments. This serves as a first-level screening of candidate actions. The top-ranked actions then enter short-window discrete event simulation refinement.

[0066] The application focus of this design is not to build a "perfect model", but to provide a stable, interpretable, and fast approximation consistent with the digital twin: the observable function mapping clarifies which physical quantities are at work; the spectral radius constraint ensures controllability within the rolling prediction window; and linear advancement enables the relative merits of hundreds or thousands of candidate actions to be given within the refresh cycle, buying time for subsequent preferential sorting and work-in-progress quota adjustments.

[0067] Example: On a production line consisting of cutting, sewing, pressing, and final inspection, the refresh cycle was set to 5 minutes and the training window to 90 minutes. The state vector contained the work-in-process (WIP) positions and queue lengths for the four processes, equipment availability and downtime indicators, and attribute pairs before and after the line change. The observable function mapping used a second-order polynomial and introduced interaction terms with the attribute pairs before and after the line change, resulting in a dimension of approximately several hundred. A sliding window was used to construct an empirical matrix and identify the Koopman operator, with the parameters automatically adjusted based on the validation error. The identified spectral radius slightly exceeded the upper bound at certain shift transitions but returned to the stable domain after shrinkage projection. A rapid evaluation was performed for two actions: "release a dark batch early and swap it with a light batch" and "maintain the current order but delay entry." Linear advancement was used to rank the WIP peak and line change cost incrementally, demonstrating that the former was more effective in reducing the ring congestion between sewing and pressing. Subsequently, a short-window simulation was performed in the digital twin, and the results were consistent with the rapid evaluation ranking. The release sequence generated based on this sorting reduces the bottleneck distance in the topology summary in subsequent windows, resulting in more balanced queue distribution and shortened recovery time after equipment downtime. Throughout the entire process, Koopman operator updates, spectral radius and contraction coefficient, and the residual distribution of the first-level evaluation are recorded, facilitating review of abnormal periods.

[0068] In the rolling forecast window, the dual price vector is calculated based on the assimilated processing time distribution, line change cost matrix, and coupling matrix. The WIP capacity upper limit is quantified as the WIP quota. The counterfactual generator is called to evaluate the incremental costs of batch release and rescheduling, and the release sequence is generated by optimizing the order. In the fixed-length rolling prediction window, the present invention uses the assimilated processing time distribution and line switching cost matrix as the parameter basis for service and switching, and the coupling matrix obtained by regularized optimal transmission as the distribution basis for demand and capacity, and establishes a dual price vector to characterize the congestion intensity of each bottleneck at each time grid. Let the bottleneck be , the time grid is , the predicted work-in-process curve is , the upper limit of capacity is The update of the dual price vector takes the form of sub-gradients: , in, is the dual price, is the step length, is a non-negative projection. To suppress short-term jitter, the coupling matrix Get the expected load of each bottleneck , accordingly Perform lightweight smoothing in time and space to keep the dual price continuous when demand and capacity change slowly.

[0069] The upper limit of WIP capacity is discretized into WIP quota, which is used as an executable constraint for release and rescheduling. Let the quota be , determined by capacity and expected load: , in, is a safety factor. If releasing or rescheduling a job causes the corresponding path's quota to exceed any bottleneck time grid, the action cannot be executed during the current cycle. The quota and the dual price form a soft and hard constraint: the former limits the amount of work-in-process that can be advanced, while the latter quantifies the marginal congestion cost of advancement.

[0070] The quality of the candidate action is measured by the incremental indicator given by the counterfactual generator. , the counterfactual generator returns the change in work-in-progress, the change in line change cost, and the change in delay, which are recorded as 、 、 The comprehensive incremental cost is defined as: , in, and is the weight used to establish a unified dimension between switching costs and delay losses. If the structural penalty has been calculated in the previous section, it will be used as Add the above formula, symbol is the structural weight, It is the incremental quantification of topology changes. In the sorting phase, the quota is feasible. Select the best from small to large to obtain the release sequence and necessary rearrangement sequence for this cycle.

[0071] This step contributes to monitoring and scheduling in three ways. First, congestion is priced. The dual price vector converts "where congestion occurs and to what extent" into additive marginal costs, facilitating comparisons across bottlenecks and time periods. Second, constraints are enforceable. WIP quotas convert abstract capacity constraints into amounts that can be consumed and returned, directly constraining the feasibility of release and rescheduling. Third, evaluation can be closed-loop. The counterfactual generator provides incremental responses consistent with the process digital twin. Combined with the dual price and WIP quota, the "evaluation-sorting-execution" chain is built on the same physical caliber.

[0072] Example: For a production line consisting of cutting, sewing, pressing, and final inspection, a rolling prediction window of 60 minutes and a step size of 5 minutes was set. The assimilated processing time distribution was used to generate service capacity curves for each bottleneck at each time grid. The coupling matrix was aggregated to obtain the expected load for each bottleneck. After calculating the dual price vector, the WIP quota was determined according to the aforementioned rules. A set of candidate actions was constructed, including partial swaps and path switches for batches to be released and batches not yet started. For each candidate action, a counterfactual generator was invoked to obtain changes in WIP, line change costs, and delays. Incremental costs were calculated using the dual price vector, line change cost weights, and delay weights. Infeasible quotas were filtered out and sorted. The resulting release sequence prioritized paths with similar attributes and lower dual prices, and the sequence was reordered to eliminate local peaks. Observations in the next window showed a decrease in the WIP peak between sewing and pressing, and a decrease in the bottleneck distance in the topology summary, indicating that congestion had eased. The dual price and WIP quota were updated with each rolling window, ensuring a stable release strategy without excessive switching.

[0073] Preferably, the dual price vector is updated using a sub-gradient rule, and spatial smoothing is performed based on the graph Laplace constructed based on the coupling matrix. When the capacity carrying distribution changes slightly, the dual price vectors of adjacent periods are temporally smoothed.

[0074] In the digital twin monitoring of multiple processes in clothing, the dual price vector is used to measure the congestion intensity of each bottleneck at each time grid, which serves as the marginal cost weight for release and rescheduling. Let the bottleneck index be , the time grid is , the work in process is predicted to be , the upper limit of capacity is , the dual price is First, update the baseline dual price in the form of sub-gradients, expressed as: , in, is the step length, This update directly maps the magnitude of the WIP overrun to the congestion intensity, ensuring interpretability and feasibility.

[0075] In order to avoid unnecessary drastic differences in the dual price in space, it is necessary to use the coupling matrix to induce similar structures between bottlenecks and perform spatial smoothing. Let the coupling matrix be ,element Representing attributes and time grid cells At the bottleneck Time grid The allocation intensity on . Define the bottleneck similarity weight within the same time grid: , This gives the Laplace matrix ,in is a diagonal matrix with the diagonal elements being the sums of the rows.

[0076] Sub-gradient results As a baseline, perform first-order graph regularization smoothing: , in, is the dual price vector of all bottlenecks in the same time grid, and L is the smoothing coefficient. The closed-form optimal solution of this objective satisfies , which can be quickly solved using conjugate gradients. Spatial smoothing makes the dual prices of bottlenecks with highly overlapping demand sources converge, reducing local jitter caused by statistical noise.

[0077] When the capacity load distribution changes little in adjacent cycles, time smoothing can be further performed to suppress cross-cycle oscillations. Let the bottleneck expected load be , the load change of adjacent cycles is measured by Wasserstein distance: , when Perform exponential time smoothing when: , in, is the change threshold, is the time smoothing coefficient. This gating ensures smooth dual price when the load pattern is stable and maintains a fast response when the load changes suddenly.

[0078] The implementation process is as follows: In each rolling forecast window, first calculate the assimilated processing time distribution and capacity upper limit and , complete the sub-gradient update to get ; Then, similarity weights and Laplace are constructed from the coupling matrix to solve the graph regularization objective and obtain ;Finally, time smoothing is performed based on the load change threshold to obtain , and put Submit it to the counterfactual evaluation and release sorting module for use.

[0079] This mechanism brings three benefits. First, stability: spatial and temporal smoothing significantly reduces high-frequency fluctuations in the dual price, preventing frequent reversals of release policies between adjacent windows. Second, consistency: price linkage is established between bottlenecks with similar demand sources, facilitating the release of work-in-progress from a globally optimal perspective. Third, interpretability: each layer of smoothing is supported by clear data, making it easier to trace the source of dual price changes during audits and replays.

[0080] Example: On a production line with two bottlenecks, sewing and ironing, the time grid is 5 minutes and the rolling prediction window is 60 minutes. The capacity limit comes from the shift calendar and equipment availability. After updating the sub-gradient, the 6th time grid is sewn Higher than the straightening. The coupling matrix calculates the overlap of the demand sources of the two bottlenecks in this grid, and the similarity weight is close to 1. After Laplace smoothing of the graph, the price difference between the two converges to half. Then, the Wasserstein distance between the adjacent cycles is calculated to be 0.02, which is lower than the threshold of 0.05. Time smoothing is performed. The value is set to 0.4. Finally, the dual price enters the release sorting process, and the system prefers to release batches with similar attributes in that time grid, while simultaneously alleviating congestion at both bottlenecks. The next window observes a decrease in the peak value of work-in-process, a reduction in the number of unnecessary line direction switches, and a decrease in the bottleneck distance in the topology summary, demonstrating that the price signal and scheduling actions form a stable closed loop.

[0081] Preferably, when the WIP capacity upper limit is quantified as WIP quota, the WIP quota is allocated according to bottlenecks and time periods, atomic locking is implemented on process paths across multiple bottlenecks, and the corresponding WIP quota is released according to the path after the job is completed.

[0082] The principle behind WIP quotas is to transform capacity constraints from static upper limits into discrete, consumable and returnable amounts, enabling both release and rescheduling across both time and path dimensions. Each bottleneck and time period is assigned a set of quotas, and the quota for each bottleneck a job passes through is locked in place, preventing congestion caused by "first-come, first-served" situations. The quota is immediately released back into the ledger once the job passes the bottleneck, maintaining a stable WIP cycle.

[0083] Quota allocation is based on the capacity limit and expected load. Let the bottleneck index be , the time period is , the upper limit of capacity is , the expected load is , the safety factor is , the work-in-process quota is .

[0084] , in, Aggregated from the coupling matrix, it indicates that the bottleneck should be allocated in this time period Expected workload; Used to leave a buffer to absorb random disturbances. Atomic locking requires a one-time check and lock of the required amount before the job enters the path. Let the job ID be , the bottleneck set involved in its process path is , the operation is at the bottleneck The set of occupied time periods is , the current occupied quota is The application amount for this time is The feasibility is determined as follows: , , If all are true, then perform atomic lock and transfer the quota from all The available balance is deducted from the locked balance; if any of the conditions is not met, the job will not be issued in this cycle to prevent inconsistent occupation across bottlenecks.

[0085] The deduction and release of the quota follows the update of the account book. Let the locking operation be recorded as , the release operation is recorded as . (Locked), when the job is in the bottleneck Time period When completed: (Release) To prevent long-term occupation, the ledger sets up a timeout recovery and abnormal rollback mechanism. The locked amount that does not trigger the completion event within the timeout will be recovered to the available balance and recorded in the evidence log for easy traceability.

[0086] The implementation process includes three key points. First, the quota ledger uses bottlenecks and time periods as keys to maintain available balances, locked balances, and historical releases, all updated with timestamps to ensure consistency with the event stream. Second, path consistency checks perform a two-phase commit before release: first pre-checking all constraints, then committing the locks all at once to ensure atomicity. Third, release rules are bound to completion and exit events, derived from event playback of the process digital twin, eliminating the need for human intervention.

[0087] This design delivers benefits in three key areas. First, it avoids mid-process congestion. Atomic locking ensures that "if you can get in, you can get out," eliminating cross-bottleneck deadlocks caused by partial locking. Second, it smooths out work-in-progress. Quotas are allocated based on bottlenecks and time periods, keeping work-in-progress peaks under control and minimizing queue fluctuations. Third, it facilitates auditing. Every lock and release transaction is timestamped and has a path anchor, enabling direct verification of release policies and exception handling.

[0088] Example: In a production line with two bottlenecks, sewing and ironing, the time segment granularity is 5 minutes. Based on the assimilated processing time distribution and the equipment calendar, calculate and According to the coupling matrix aggregation, we can get and Pick calculate . A homework The path goes through sewing and ironing in sequence. It is expected that the third and fourth time periods of sewing will occupy 1 unit of quota each, and the fifth time period of ironing will occupy 1 unit of quota, forming , , After the system checks that the balances at the three locations meet the feasibility requirements, it executes atomic locking and deducts the balances from the three locations simultaneously. ) and (sewing, ) release the quota, when the ironing is completed (iron, ) release quota. If a timeout occurs during ironing due to equipment failure, the timeout recovery rule returns the locked quota to the available balance and marks the job as abnormal, placing it on the scheduling avoidance list for the next cycle. During this cycle, the peak value of the sewing entrance queue decreased, no new waiting queues appeared at the ironing entrance, and the loop persistence in the topology summary decreased, indicating that atomic locking and path-based release effectively suppressed work-in-process backflow and localized loops.

[0089] Preferably, the incremental cost is composed of the product of the dual price and the change in work-in-process, the incremental term of the line change cost, the incremental term of the delay cost and the weighted structural penalty term based on the topological structure summary, and adopts a two-level evaluation process, in which the first level is a fast evaluation based on the Koopman operator and the second level is a short-window discrete event simulation refinement evaluation.

[0090] This invention quantifies the impact of candidate actions into a single scalar to support comparable ranking within a rolling prediction window. Candidate actions include batch release, batch rescheduling, process path switching, and line change direction selection. The design concept aggregates the three costs of congestion, switching, and delivery into a single caliber, while penalizing "structural degradation" to avoid the accumulation of ring congestion caused by local optimality.

[0091] The core incremental cost is defined as: , in, Number the candidate actions; bottleneck In the time grid The dual price represents the marginal congestion cost of a unit of work-in-progress at that location; For action The amount of change in the work-in-progress caused by this; For action The resulting incremental cost of line switching is calculated based on the line switching cost matrix and the attribute pairs before and after the line switching; For action The increment of delivery delay is based on the aggregation of the difference between the batch delivery date and the expected completion time; For action Quantification of topological deterioration, derived from the topological summary; The weights are used to map costs of different dimensions to a unified scale. The product of the dual price and the change in work-in-process reflects the marginal impact of "where to push the work-in-process"; the line change and delay terms reflect the direct costs of "switching and delivery"; and the structural penalty term inhibits actions that lead to high-persistence loops or increase the bottleneck distance.

[0092] The two-level evaluation process is as follows. The first level is a fast evaluation, which uses the Koopman operator to linearly advance the state in a short period of time to obtain the approximate value of the observable function of the state vector after several steps, and then maps it into the change of work-in-progress, the change of line change cost and the change of delay, forming The rapid evaluation covers all candidates and is completed within the refresh cycle, producing a reliable relative ranking. The second level is a refined evaluation, which performs short-window discrete event simulation on the colored delay Petri net for a small number of actions ranked at the first level. The service time and line change time are taken from the assimilated processing time distribution and line change cost matrix to obtain high-fidelity 、 、 , and recalculate the topological structure summary based on the work-in-process flow graph of the counterfactual path, and obtain If the deviation between the refined result and the quick result exceeds the threshold, the refined result will take precedence and overwrite the quick value.

[0093] The calibers for obtaining each increment are as follows: WIP changes are obtained by differentially comparing the state before and after the rapid advancement or refinement simulation; the line change cost increment is based on the cut sequence triggered by the action and the attribute pairs before and after the line change, and the attribute pairs involved are substituted into the line change cost matrix one by one and summed; the delay increment is based on the batch delivery set, and the part that exceeds the expected completion time is aggregated by non-negative differentials; the structural penalty is extracted from the topological structure summary, using the change in bottleneck distance or maximum persistence of adjacent windows as an indicator, and is defined as: , in, For action Summary of future window topology under, is the summary of future window topology for the baseline scenario, is the bottleneck distance, is the window step size. Taking the non-negative part ensures that only "worse" structural changes are penalized. Weight , , The company's established switching costs, delivery losses and structural risk preferences can be calibrated on a weekly rolling basis.

[0094] To ensure that the sorting is executable, all candidates must pass the feasibility check of the work-in-progress quota and process path constraints before pricing, and those that are not feasible will be directly eliminated. After the sorting is completed, the release sequence and the necessary rearrangement sequence will be output; if multiple If they are close, the tie is broken in the order of "smaller structural penalty first, smaller line change cost first".

[0095] This effectiveness is reflected in three key areas. First, comparability: Different types of actions are compared using a unified metric, avoiding the bias of single-metric approaches such as focusing solely on queue length or handoff count. Second, low latency: The two-level evaluation process places the majority of computational effort on the fast layer, while the refined layer only covers the top few nodes, ensuring compliance within the rolling window. Third, robustness: Structural penalties suppress potential accumulation of ring congestion, preventing short-term gains from leading to long-term degradation.

[0096] Example: In a production line that includes sewing and ironing, the rolling prediction window is 60 minutes and the step size is 5 minutes. Construct a candidate action set, including three categories: early release of a dark batch, swapping with a light batch, and maintaining the order but delaying entry. The first-level evaluation uses the Koopman operator to advance to the next 6 steps, and obtains the approximate increments of the three types of actions: early release of the work-in-process peak value decreases, the line change cost increases slightly, and the delay decreases; swapping the work-in-process peak value decreases more, but the line change cost increases significantly; delaying the entry of the work-in-process peak value decreases slightly and the delay increases. Combined with the current dual price vector and weight, The sorting is "early release" and "delayed entry" and "swap". Select the first two items to enter the refinement simulation and get 、 、 , and calculate the high-fidelity value of : Early release reduces the bottleneck distance and the structural penalty is 0; delayed entry does not deteriorate the structure and the penalty is 0. Maintaining the same order. The system generates a release sequence based on this: releasing the dark-colored batch first, then maintaining the original order for the remaining batches. The peak WIP in the next window, between sewing and ironing, decreased, and the bottleneck distance in the topology summary decreased, with no additional line direction changes. A two-level evaluation log records the differences between the rapid and refined phases, along with the basis for acceptance, facilitating audits and review.

[0097] The process path is locked and issued according to the WIP quota, reversible fine-tuning is implemented based on the deviation between the expected state and the execution state, and withdrawal and path rerouting are triggered based on the topology summary.

[0098] The present invention places capacity constraints at the executable level: the WIP capacity limit is discretized into WIP quotas, which are stored in the ledger using "bottleneck-time period" as the key. Before entering the process path, the job performs a consistency check and atomically locks the quotas of all bottlenecks and time periods on its path at once, ensuring that "if you enter, you can complete it." Let the job be identified as , the bottleneck set is , the operation is at the bottleneck The set of occupied time periods is The application amount is , the current occupied quota is , the work-in-process quota is The feasibility and atomic locking conditions are: When satisfied, in all The quota is deducted synchronously and a lock record is generated. After the corresponding bottleneck is completed, the quota is released step by step along the path. The ledger and event stream are aligned through timestamps to form an auditable track.

[0099] In order to suppress the accumulation of deviations during execution, reversible fine-tuning is introduced. The expected state is given by the counterfactual fast evaluation in a short time step, and the execution state comes from the event stream replay. The expected state is , the execution status is , the weight matrix is (used to unify the dimensions of different state components), the deviation measure is: , when When the threshold is exceeded, the fine-tuning action set (partial swap of unstarted batches, delayed release, and batch fine-tuning) is triggered. The advantages and disadvantages of the above are based on the incremental cost defined above. After evaluation and adding quota feasibility and path consistency constraints, the optimal action is: Atomic locking is feasible and does not change the continuity of the work that has already started. Fine-tuning is first verified in the digital twin in the form of a shadow work order and then officially issued. If the verification fails, it will be withdrawn immediately without changing the account balance.

[0100] At the structural level, a trigger mechanism based on topological structure summary is used to control retraction and path diversion. The topological distance between adjacent windows is , the maximum persistence is .when or When a process is called, the system generates a recall list for unstarted batches on high-durability loops, fully refunds the locked-in amount based on the path, selects an alternative path from the set of feasible process paths based on the principle of minimizing incremental cost, and issues a rerouting instruction. For already started operations, only the subsequent partial adjustments to the rerouting process are performed, without interrupting the current process.

[0101] The comprehensive effects of this design are reflected in the following aspects: First, quota-path consistency ensures that release and rescheduling naturally meet capacity constraints, avoiding the "first occupied, then empty" situation across bottlenecks; second, a closed-loop deviation mechanism ensures that the expected-actual deviation during the execution period is reversibly corrected within the current cycle to prevent error propagation; third, structural protection ensures that topology triggering converts structural risks such as "deepening ring congestion" into clear withdrawal and rerouting actions, reducing the probability of oscillation and deadlock; fourth, strong auditability ensures that locking, release, withdrawal, and rerouting are all bound to specific event fragments for easy traceability.

[0102] Example: In a production line that includes sewing and ironing, the time period granularity is 5 minutes and the rolling forecast window is 60 minutes. The WIP quota is calculated based on the capacity limit and expected load and written into the ledger. The plan involved sewing in time periods 3 and 4 and ironing in time period 5. After the quota check satisfied the atomic lock conditions, the quotas for the three locations were simultaneously deducted and a work order was issued. During time period 4, the expected-actual deviation (ete_tet) increased due to a brief ironing downtime. The system generated two possible fine-tuning options: swapping the unused light-colored batches or delaying the current dark-colored batch by one time period. Based on an assessment of incremental cost and quota feasibility, the delay option offered the lowest incremental cost and did not require an increase in line change costs. The system then verified the delay with a shadow work order and officially issued the order. The topology summary then revealed that the bottleneck distance between the sewing buffer and the ironing entrance had risen above a threshold, triggering a structural guard. The unused light-colored batches upstream of the loop were partially withdrawn, the corresponding quota was refunded, and an alternative path with the same color as the previous one was selected. At the end of this cycle, the peak work-in-process (WIP) between sewing and ironing decreased, the number of line change switches decreased, and the topological distance decreased. All lock and release records and action decisions were recorded in the evidence log for subsequent review.

[0103] Preferably, reversible fine-tuning includes batch swapping and entry delay operations for batches that have not yet started. The triggering conditions for withdrawal and path rerouting are that the structural index of the topological structure summary exceeds the threshold. Path rerouting selects an alternative path from the set of feasible process paths based on the principle of minimum incremental cost.

[0104] The principle of reversible fine-tuning is to apply minimal perturbations to unstarted batches without interrupting ongoing work, realigning the WIP distribution with the desired trajectory while adhering to WIP quotas and process path constraints. The desired trajectory is derived from counterfactual rapid evaluation, and the execution status is derived from event stream replay. A weighted deviation is used to characterize execution deviation and serves as the trigger for fine-tuning: , in, For the moment The execution state vector of is the expected state vector, is the weight matrix of each state component. If the threshold is exceeded, a candidate action set for the unstarted batch is generated at the corresponding bottleneck entrance, including two types of actions: batch swap and inbound delay. Each candidate action is verified in the digital twin with a shadow work order, and is officially issued after passing the verification. If the verification fails, it is withdrawn, and the account balance and work-in-progress quota remain unchanged. The quality of the candidate action is determined by the incremental cost defined above. Unify the metrics and select the best one based on the WIP quota and atomic lock feasibility. The candidate action set is denoted as , the feasible solution is The feasibility check for WIP quotas and atomic locks is performed. The feasibility check follows the previously described determination of quota balances and is not repeated here. The swap operation swaps the queue positions of two batches within the same bottleneck and time period; the inbound delay operation postpones the inbound time of a single batch by a certain number of grids. Neither operation changes the process continuity of the already started batches.

[0105] Retraction and path rerouting are triggered by the threshold crossing of the structure indicator of the topology summary. Let the topology summary of the current window and the previous window be and , the bottleneck distance is , the maximum persistence is The trigger criteria are , in, and After the triggering, first locate the unstarted batch on the high persistence ring based on the contribution edge set, generate a withdrawal list, and return the locked amount according to the path; then select an alternative path for each withdrawn batch in the feasible process path set, and record the feasible path set as , the path selection is Feasibility check via WIP quota and atomic lock, where For batch Adoption Path The alternative path is only executed on the batches that have not started. For the batches that have started, only the subsequent unstarted sections are partially rerouted without interrupting the current processing.

[0106] The key points of implementing this mechanism include three aspects. First, fine-tuning precedes withdrawal: when the deviation is caused by a short-term disturbance, batch swapping and inbound delay are used to quickly reset it to avoid frequent withdrawals at the structural level. Second, the entire action process is reversible: if the shadow work order fails to pass the verification, it will be withdrawn, and there will be no permanent impact on the work-in-progress quota and account balance; the formally issued action will only affect the batches that have not started. Third, the path selection is executable: the generation and screening of alternative paths and the process of digital twins Figure 1 This satisfies both the sequence relationship and the WIP quota and atomic locking constraints, avoiding the situation of "first occupied and then empty" after the route is changed.

[0107] The application effect is reflected in four aspects. First, deviation suppression: reversible fine-tuning eliminates the deviation between expectations and execution within a single cycle, reducing cross-cycle accumulation. Second, congestion elimination: when the structural indicators rise, withdrawal and rerouting transfer the load from the loop channel to the alternative channel. Combined with the WIP quota and dual price, the ring congestion can be sustainably reduced. Third, stable release: the order of fine-tuning first and then withdrawing reduces the high-frequency jitter of the release strategy, and the release sequence changes are more stable. Fourth, auditability: each swap, delay, withdrawal and rerouting action is accompanied by a timestamp, WIP quota change record and incremental cost details, which facilitates responsibility tracing and strategy review.

[0108] Example: On a production line that includes sewing and ironing, the time grid is 5 minutes and the rolling forecast window is 60 minutes. In the 12th grid, a short ironing stoppage causes a deviation between expectations and execution. The system generates two reversible fine-tuning candidates at the ironing entrance: swapping the second and third unstarted batches in the queue, or delaying the second batch by one grid. Calling the counterfactual quick evaluation to obtain the two The incremental cost of the delay solution is smaller and it passes the quota and atomic lock check. The system verifies it with a shadow work order and then officially issues it. In the next window, the bottleneck distance of the topology summary rises above the threshold, triggering the structure guard, generating a withdrawal list for the unstarted batches located in the "sewing buffer-ironing entrance-ironing buffer-sewing entrance" loop, returning their locked quota according to the path, and based on the feasible process path set Select an alternative route for the same fabric as the current one. After execution, the next window observed a decrease in the peak WIP volume, a reduction in the number of line direction changes, and a decrease in the bottleneck distance. Shadow verification results for all actions, along with official release times, deductions and refunds of WIP quotas, are recorded in the evidence log for subsequent review.

[0109] The above are merely embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should be included within the scope of the claims of the present application.

Claims

1. A digital twin monitoring method for multiple processes of clothing, characterized in that: The following steps are involved: A digital twin of the process, represented by a colored time-delay Petri net, is established. Production signals are mapped into event streams according to a unified event dictionary. The initial state is determined through event playback, and the line change cost matrix is ​​estimated based on this. Hierarchical online assimilation of event streams is performed to update the processing time distribution and line change cost matrix. A topological structure summary is generated based on the work-in-process flow graph. The predicted arrival flow and capacity load distribution are constructed and the coupling matrix is ​​solved through regularized optimal transmission. The Koopman operator is identified to form a counterfactual generator. In the rolling forecast window, the dual price vector is calculated based on the assimilated processing time distribution, line change cost matrix, and coupling matrix. The WIP capacity upper limit is quantified as the WIP quota. The counterfactual generator is called to evaluate the incremental costs of batch release and rescheduling, and the release sequence is generated by optimizing the order. The process path is locked and issued according to the WIP quota, reversible fine-tuning is implemented based on the deviation between the expected state and the execution state, and withdrawal and path rerouting are triggered based on the topology summary.

2. The method according to claim 1, characterized in that Event replay and place invariant consistency check are used to determine the initial state, so that the process digital twin and the event stream maintain conservation and consistency in the number of tags and flow direction.

3. The method according to claim 1, characterized in that Hierarchical online assimilation updates parameters at the equipment level, workstation level, product level, and batch level, and applies robust weighting to abnormal observations in the event stream to suppress the offset impact on the processing time distribution and the line change cost matrix.

4. The method according to claim 1, wherein The topology summary is obtained by persistent homology calculation on the work-in-progress flow graph, and the topology change is measured by the bottleneck distance between adjacent time windows, which is used to trigger withdrawal and path rerouting.

5. The method according to claim 1, wherein The cost matrix of regularized optimal transmission is composed of the weighted measures of product attribute differences and the normalized values ​​of the line change cost matrix, and the coupling matrix is ​​solved through Sinkhorn iteration.

6. The method according to claim 1, characterized in that The identification of the Koopman operator is based on the observable function mapping of the state vector, which includes the polynomial expansion of the WIP position, queue length, equipment status and attribute pairs before and after the line change, and the stability of the counterfactual generator is guaranteed by the spectral radius constraint.

7. The method according to claim 1, characterized in that The dual price vector is updated using the sub-gradient rule and spatially smoothed based on the graph Laplace constructed based on the coupling matrix. When the capacity carrying distribution changes slightly, the dual price vectors of adjacent periods are temporally smoothed.

8. The method according to claim 1, characterized in that When the upper limit of WIP capacity is quantified as WIP quota, the WIP quota is allocated according to bottlenecks and time periods, atomic locking is implemented on process paths that cross multiple bottlenecks, and the corresponding WIP quota is released according to the path after the job is completed.

9. The method according to claim 1, characterized in that The incremental cost is composed of the product of the dual price and the change in work-in-process, the incremental term of the line change cost, the incremental term of the delay cost and the weighted structural penalty term based on the topological structure summary. A two-level evaluation process is adopted, in which the first level is a fast evaluation based on the Koopman operator and the second level is a short-window discrete event simulation refinement evaluation.

10. The method according to claim 1, characterized in that Reversible fine-tuning includes batch swapping and inbound delay operations for batches that have not yet started. The triggering conditions for withdrawal and path rerouting are that the structural indicators of the topological structure summary exceed the threshold. Path rerouting selects an alternative path from the set of feasible process paths based on the principle of minimum incremental cost.

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